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# Probability, basic principles

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This problems is from 400 level probability class but introductory course. Please specify the terms you use (if necessary) and explain each step of your solutions. Thank you very much.

18. 45% of the students at U of M do neither have a tattoo nor a body piercing (other than an ear piercing). 40% of the students at U of M have a tattoo. 30% of the students at U of M have a body piercing. One student is randomly selected, what is the probability that this student has
a. a tattoo or a body piercing?
b. a tattoo and a body piercing?
c. only a tattoo or only a body piercing?

https://brainmass.com/math/probability/probability-events-32746

## SOLUTION This solution is FREE courtesy of BrainMass!

In this solution, probabilities of the events in question are found using basic priciples of probability. Please see the attached Word document for the solution.

18. 45% of the students at U of M do neither have a tattoo nor a body piercing (other than an ear piercing). 40% of the students at U of M have a tattoo. 30% of the students at U of M have a body piercing. One student is randomly selected, what is the probability that this student has
a. a tattoo or a body piercing?
b. a tattoo and a body piercing?
c. only a tattoo or only a body piercing?

Let T: Has a Tattoo
B: Has a Body Piercing

These are given in the problem:

a.

The complement rule gives you the probability.

b.

The additive law of probability gives you this probability.

c.

The probability of only one of the two events is the union minus the intersection.

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